The worst case complexity of McDiarmid and Reed's variant of BOTTOM-UP HEAPSORT is less than n log n + 1.1n

Authors:
Ingo Wegener
Affiliations:
Fachbereich Informatik, LS II, Universität Dortmund, Postfach 500 500, 4600 Dortmund 50, Germany
Venue:
Information and Computation
Year:
1992

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Abstract

BOTTOM-UP HEAPSORT is a variant of HEAPSORT which beats on average even the clever variants of QUICKSORT, if n is not very small. Up to now, the worst case complexity of BOTTOM-UP HEAPSORT has been able to be estimated only by 1.5n log n. McDiarmid and Reed (1989) have presented a variant of BOTTOM-UP HEAPSORT which needs extra storage for n bits. The worst case number of comparisons of this (almost internal) sorting algorithm is estimated by n log n + 1.1 n. It is discussed how many comparisons can be saved on average.